b. I like to listen to rock music while I do my homework
Explanation:
In the sentence (a) the conjunction is missing. A conjunction is a word which joins two words or sentences. The word 'while' is used as a conjunction to join the two sentences. In the sentence (b) the two sentences are joined by the conjunction 'while' which helps in making complete sense of the sentence.
I would think that "insensitive" meant that his other girlfriends thought he didn't care, or he was a total idiot or soemthing. Just something like that. I hope this helped a little bit love!